WASHINGTON — The Senate Intelligence Committee has issued a subpoena to compel Michael D. Cohen, President Trump’s former lawyer, to appear before the panel next month to formally correct false testimony that he delivered last year about a proposed Trump Organization project in Moscow, one of his lawyers confirmed on Thursday.

The subpoena was disclosed a day after Mr. Cohen pulled out of a public hearing scheduled for Feb. 7 before the House Oversight and Reform Committee, citing in a letter from his lawyer, Lanny J. Davis, verbal attacks by Mr. Trump.

Mr. Cohen’s initial agreement to appear before the Oversight Committee had been voluntary, but he will have little choice in complying with the Senate request. Democrats in charge of the House Oversight and Intelligence committees have signaled in recent days that they may follow suit and issue subpoenas of their own, despite acknowledging Mr. Cohen’s safety concerns.

Unlike the Oversight session, Mr. Cohen’s return to the Senate Intelligence Committee will almost certainly be behind closed doors. The panel has conducted a wide-ranging investigation of Russia’s election interference campaign, and possible ties to the Trump campaign, for roughly two years now largely out of the public eye.

Mr. Cohen has appeared before the Senate Intelligence Committee twice before behind closed doors. In one case, the panel’s leaders abruptly cut short the session after learning that he had shared with reporters a written opening statement he would deliver in private — testimony that would later prove to have contained falsehoods about a Trump Organization proposal to build a skyscraper in Moscow. He was later brought back for a closed-door session with Senate investigators, the details of which have remained secret. (Mr. Cohen also made false statements to the House Intelligence Committee, according to the special counsel.)

Since his guilty plea in late November for lying to Congress, Senate Intelligence Committee officials have worked with Mr. Cohen and his lawyers to try to secure a return visit voluntarily so he can correct his false testimony and answer other questions pertinent to the panel’s investigation. But those talks were unproductive, even as Mr. Cohen agreed to appear publicly before another congressional panel.

Spokeswomen for the intelligence committee’s top Republican and Democrat both declined to comment, and Mr. Davis did not elaborate beyond confirming receipt of the subpoena, which was first reported by CNN.

The back and forth over Mr. Cohen’s testimony was the cause of continued sniping on Thursday between Mr. Trump and Mr. Davis. The president linked Mr. Cohen to his one-time Democratic political rival, Hillary Clinton, a pairing that seemed designed to excite his core voters.

In an early morning Twitter post, Mr. Trump described Mr. Cohen as a “bad lawyer” and reminded the public about Mrs. Clinton’s 2016 interview with the F.B.I., the circumstances of which have become part of a litany of anti-Clinton narratives that cast the investigation into her use of a private server as flawed.

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President Trump at the White House on Wednesday.CreditDoug Mills/The New York Times

The second lawyer to whom Mr. Trump alludes without naming is most likely Mr. Davis, a Washington attorney and close ally of the Clintons, who is currently representing Mr. Cohen.

In an interview on Thursday, Mr. Davis accused Mr. Trump’s current personal lawyer, Rudolph W. Giuliani, of witness tampering for recent comments he made about Mr. Cohen’s father-in-law, suggesting he might have ties to organized crime. Earlier this week, Mr. Cohen canceled his plans to testify publicly before Congress next month, citing concerns about his family’s safety.

Mr. Trump has previously raised the notion that Mr. Cohen’s father-in-law, Fima Shusterman, a Ukrainian immigrant, has ties to organized crime, but there has been no evidence to back up those claims. Mr. Shusterman pleaded guilty in 1993 of trying to evade federal income reporting requirements and was sentenced to probation.

“Mr. Trump has immunity from indictments, so it’s alleged or argued in the Justice Department,” Mr. Davis said on Thursday in an interview with ABC’s “Good Morning America.” “But Mr. Giuliani has committed a crime or at least should be indicted for that crime on the face of what he said on national television.”

Mr. Giuliani responded on Thursday, saying that the president’s remarks were “more than sufficient” to answer those claims.

Mr. Trump and his advisers had been focused on what Mr. Cohen might have said to Congress that could further damage the president’s image and possibly present new legal problems. Republicans, however, were eager for Mr. Cohen to testify in public, saying privately that they planned to question him aggressively and paint him as a liar.

Top House Democrats have already warned Mr. Trump about witness tampering after the president made comments earlier this month accusing Mr. Cohen of lying in an effort to get a better deal with federal prosecutors.

On Wednesday, Representative Elijah E. Cummings of Maryland, who leads the Oversight and Reform Committee, and Representative Adam B. Schiff of California, the chairman of the Intelligence Committee, said they understood Mr. Cohen’s concerns for his family’s safety and repeated their earlier warning against efforts to intimidate witnesses, which is against the law.

Mrs. Clinton, now a private citizen, continues to be a favorite target of Mr. Trump and some of his supporters who have chanted “lock her up” at rallies nearly two years after she lost the presidential election.

A version of this article appears in print on , on Page A15 of the New York edition with the headline: Senate Intelligence Panel Subpoenas Cohen to Testify About Trump Project. Order Reprints | Today’s Paper | Subscribe